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Given that the cameras have been calibrated and
the two perspective projection matrices
C =[qij] and C'=[q'ij]
are known,
then for any scene point M with unknown 3-D coordinates
(X,Y,Z), that projects onto
the two retinal planes at (u,v) and (u',v'), we have
![\begin{displaymath}
\mbox{\bf C} \left[ \begin{array}
{c} X \\ Y \\ Z \\ 1 \e...
...t[ \begin{array}
{c} s' u' \\ s' v' \\ s' \end{array}\right].\end{displaymath}](img34.gif)
Eliminating s and s' and combining the two equations
into matrix form gives
![\begin{displaymath}
\left[ \begin{array}
{ccc}
q_{11}-uq_{31} & q_{12}-uq_{32} ...
...- q_{24} \\ u' - q'_{14} \\ v' - q'_{24}
\end{array}\right].\end{displaymath}](img35.gif)
This is a linear system in (X,Y,Z). The 3-D coordinates of M
can be easily computed.
Robyn Owens
10/29/1997